A subsonic load for the .223 is essentially pointless. What you end up with is basically a very unwieldy process for duplicating the performance of a subsonic .22LR. It won't cycle and it won't do much more than a .22LR itself.
A better approach would be setting up the AR with a .22LR conversion, then feeding it with standard (subsonic) velocity .22LR ammunition. At least it will function effectively, and you'll have something that's capable of defeating small-medium sized rodents.
This very same question comes up time after time after time here. The general gist of the discussion boils down to what I have just presented you.
Greg